**NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1****NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.2**

**NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.2 ****(Rationalised Contents)**

**Ex 5.2 Class 7 Maths Question 1.**

State the property that is used in each of the
following statements?(i) If a || b, then

∠1 = ∠5

(ii) If ∠4 = ∠6, then a || b

(iii) If ∠4 + ∠5 = 180°, then a || b

**Solution:
**(i) We have a || b

∴ ∠1 = ∠5

**Property used:**
If two lines are parallel and cut by a transversal, then the pairs of
corresponding angles are equal.

(ii) We have ∠4 = ∠6

∴ a || b

**Property used: **If
a pair of alternate angles are equal, then the lines are parallel.

(iii) We have ∠4 + ∠5 = 180°

∴ a || b

**Property used: **If
the sum of the co-interior angles is 180°, then the lines are parallel.

**Ex 5.2 Class 7 Maths Question 2.**

In the given figure, identify(i) the pairs of corresponding angles.

(ii) the pairs of alternate interior angles.

(iii) the pairs of interior angles on the same side of the transversal.

**Solution:
**(i) The pairs of corresponding angles are: ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8, ∠3 and ∠7.

(ii) The pairs of alternate interior angles are: ∠2 and ∠8, ∠3 and ∠5.

(iii) The pairs of interior angles on the same side of the transversal are: ∠2 and ∠5, ∠3 and ∠8.

(iv) The vertically opposite angles are: ∠1 and ∠3, ∠2 and ∠4, ∠5 and ∠7, ∠6 and ∠8.

**Ex 5.2 Class 7 Maths Question 3.**

In the given figure, p || q. Find
the unknown angles.**Solution:****
**∠e + 125° = 180° (Linear pair of angles)

∴ ∠e = 180° – 125° = 55°

∠e = ∠f (Vertically opposite angles)

∴ ∠f = 55°

∠a = ∠f = 55° (Alternate interior angles)

∠c = ∠a = 55° (Vertically opposite angles)

∠d = 125° (Corresponding angles)

∠b = ∠d = 125° (Vertically opposite angles)

Thus, ∠a = 55°, ∠b = 125°, ∠c = 55°, ∠d = 125°, ∠e = 55°, ∠f = 55°.

**Ex 5.2 Class 7 Maths Question 4.**

Find the value of x in each of the
following figures, if *l*||

*m*.

**Solution:**

(i) Let the vertically opposite angle of 110° be y.

∴ y = 110° (Vertically opposite angles)

∠x + ∠y = 180° (Sum of interior angle on the same side of transversal)

∠x + 110° = 180° .

∴ ∠x = 180° – 110° = 70°

Thus, x = 70°

(ii) ∠x = 100° (Pair of corresponding angles)

**Ex 5.2 Class 7 Maths Question 5.**

In the given figure, the arms of
two angles are parallel. If ∠ABC = 70°, then find(i) ∠DGC

(ii) ∠DEF

**Solution:**

Given: AB || DE and BC || EF

∠ABC = 70°

(i) ∠DGC = ∠ABC (Pair of corresponding angles)

∠DGC = 70°

(ii) ∠DEF = ∠DGC

∠DEF = 70° (Pair of corresponding angles)

**Ex 5.2 Class 7 Maths Question 6.**

In the given figure below, decide
whether *l*is parallel to

*m*.

**Solution:**

(i) The sum of the interior angles on the same side of transversal

= 126° + 44° = 170° ≠ 180°

∴

*l*is not parallel to

*m*.

(ii) Let the angle opposite to 75° be x.

x = 75° (Vertically
opposite angles)

∴ The sum of the interior angles on the same side of transversal

= x + 75° = 75° + 75° = 150° ≠ 180°

∴ *l* is not parallel to *m*.

(iii) Let the angle opposite to 57° be y.

∴ ∠y = 57° (Vertically
opposite angles)

∴ The sum of the interior angles on the same side of transversal

= 57° + 123° = 180°

∴ *l* is parallel to *m*.

(iv) Let the angle opposite to 72° be z.

∴ z = 70° (Vertically
opposite angles)

∴ The sum of the interior angles on the same side of transversal

= z + 98° = 72° + 98° = 170° ≠ 180°

∴ *l* is not parallel to *m*.

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